Over the last decade, impressive progress was made
in designing potentials from electronic structure calculations using
supervised Machine Learning (ML) methods
[1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}.
There are now standard libraries for the ML training [8]}
that can be used in combination with molecular dynamics (MD)
simulation packages [9]} such as LAMMPS [10]}
or in combination with workflow softwares such as ASE [11]}.
On-the-fly ML force field methods have been also proposed [12]}
and implemented directly into ab initio codes in order to
bypass most of electronic-structure calculation steps [13]}.
Different ML techniques have been used, ranging from simple linear
regression (LR) methods such as the spectral neighbor analysis
potential (SNAP) method [14]}, [6]} to highly
non-linear regression methods using High Dimensional Neural Networks
[16]}, [8]} (HDNN) or Kernel Regression (KR)
[18]}, [19]}, [20]}. The designed potentials
reach in general an accuracy close to the ab initio
calculations from which the database was formed, with exceptional
results for the description of relative stability between crystalline
phases [21]} and defects [22]}. However,
approaches taking full account of liquid and
crystalline states remain scarce [21]}, [24]}
and are often limited to the objective of a good description of the
melting point. The main reason for this stems from the fact that
the chosen ab initio configurations should cover all
situations, as ML techniques may become less reliable outside the
training domain [1]}. It becomes even more crucial for
crystal nucleation occurring under deep undercooling conditions
with a strong evolution of the liquid structure with respect to
that above melting, showing an increasing icosahedral [26]}
ordering and structural heterogeneity [27]} triggering
homogeneous nucleation [28]}.
